Производная (x-2)^sin(x)

Вы ввели

       sin(x)
(x - 2)      

$$\left(x - 2\right)^{\sin{\left (x \right )}}$$

Подробное решение

1. Не могу найти шаги в поиске этой производной.

   Но производная

   $\left(\log{\left (\sin{\left (x \right )} \right )} + 1\right) \sin^{\sin{\left (x \right )}}{\left (x \right )}$

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Ответ:

$\left(\log{\left (\sin{\left (x \right )} \right )} + 1\right) \sin^{\sin{\left (x \right )}}{\left (x \right )}$

Первая производная

       sin(x) /sin(x)                    \
(x - 2)      *|------ + cos(x)*log(x - 2)|
              \x - 2                     /

$$\left(x - 2\right)^{\sin{\left (x \right )}} \left(\log{\left (x - 2 \right )} \cos{\left (x \right )} + \frac{\sin{\left (x \right )}}{x - 2}\right)$$

Вторая производная

               /                             2                                            \
        sin(x) |/sin(x)                     \      sin(x)                         2*cos(x)|
(-2 + x)      *||------ + cos(x)*log(-2 + x)|  - --------- - log(-2 + x)*sin(x) + --------|
               |\-2 + x                     /            2                         -2 + x |
               \                                 (-2 + x)                                 /

$$\left(x - 2\right)^{\sin{\left (x \right )}} \left(\left(\log{\left (x - 2 \right )} \cos{\left (x \right )} + \frac{\sin{\left (x \right )}}{x - 2}\right)^{2} - \log{\left (x - 2 \right )} \sin{\left (x \right )} + \frac{2 \cos{\left (x \right )}}{x - 2} - \frac{\sin{\left (x \right )}}{\left(x - 2\right)^{2}}\right)$$

Третья производная

               /                             3                                                                                                                                      \
        sin(x) |/sin(x)                     \                         3*sin(x)    3*cos(x)     /sin(x)                     \ /  sin(x)                         2*cos(x)\    2*sin(x)|
(-2 + x)      *||------ + cos(x)*log(-2 + x)|  - cos(x)*log(-2 + x) - -------- - --------- - 3*|------ + cos(x)*log(-2 + x)|*|--------- + log(-2 + x)*sin(x) - --------| + ---------|
               |\-2 + x                     /                          -2 + x            2     \-2 + x                     / |        2                         -2 + x |           3|
               \                                                                 (-2 + x)                                    \(-2 + x)                                 /   (-2 + x) /

$$\left(x - 2\right)^{\sin{\left (x \right )}} \left(\left(\log{\left (x - 2 \right )} \cos{\left (x \right )} + \frac{\sin{\left (x \right )}}{x - 2}\right)^{3} - 3 \left(\log{\left (x - 2 \right )} \cos{\left (x \right )} + \frac{\sin{\left (x \right )}}{x - 2}\right) \left(\log{\left (x - 2 \right )} \sin{\left (x \right )} - \frac{2 \cos{\left (x \right )}}{x - 2} + \frac{\sin{\left (x \right )}}{\left(x - 2\right)^{2}}\right) - \log{\left (x - 2 \right )} \cos{\left (x \right )} - \frac{3 \sin{\left (x \right )}}{x - 2} - \frac{3 \cos{\left (x \right )}}{\left(x - 2\right)^{2}} + \frac{2 \sin{\left (x \right )}}{\left(x - 2\right)^{3}}\right)$$